Cross-drainage and drop structures

Transcription

1 Chapter 10 Cross-drainage and drop structures 10.1 Aqueducts and canal inlets and outlets Introduction The alignment of a canal invariably meets a number of natural streams (drains) and other structures such as roads and railways, and may sometimes have to cross valleys. Cross-drainage works are the structures which make such crossings possible. They are generally very costly, and should be avoided if possible by changing the canal alignment and/or by diverting the drains Aqueducts An aqueduct is a cross-drainage structure constructed where the drainage flood level is below the bed of the canal. Small drains may be taken under the canal and banks by a concrete or masonry barrel (culvert), whereas in the case of stream crossings it may be economical to flume the canal over the stream (e.g. using a concrete trough, Fig.10.1(a)). When both canal and drain meet more or less at the same level the drain may be passed through an inverted siphon aqueduct (Fig. 10.1(d)) underneath the canal; the flow through the aqueduct here is always under pressure. If the drainage discharge is heavily silt laden a silt ejector should be provided at the upstream end of the siphon aqueduct; a trash rack is also essential if the stream carries floating debris which may otherwise choke the entrance to the aqueduct.

2 AQUEDUCTS AND CANAL INLETS AND OUTLETS 419 Fig Layout of an aqueduct Superpassage In this type of cross-drainage work, the natural drain runs above the canal, the canal under the drain always having a free surface flow. The superpassage is called a canal siphon or simply an inverted siphon if the canal bed under the drain is lowered to accommodate the canal flow, which will

3 420 CROSS-DRAINAGE AND DROP STRUCTURES always be under pressure. The layouts of the superpassage and canal siphon are similar to those shown in Figs10.1(a) and 10.1(b), with the canal and drain interchanged Level crossing Level crossing facilities are provided when both the drain and the canal run at more or less the same level. This is more frequently used if either of the flows occurs for a short period (e.g. flash floods in the drain); in addition, the mixing of the two bodies of water must also be acceptable (quality considerations). The plan layout of a level crossing with two sets of regulators, one across the drain and the other across the canal, is shown in Fig Normally, the canal regulator regulates its flow with the drain regulator kept closed. Whenever the flash floods occur, the canal gates are closed and drainage gates opened to let the flood flow pass Canal inlets and outlets When the drainage flow is small it may be absorbed into the canal through inlets. The flow in the canal may be balanced, if necessary (in the case of small canals), by providing suitable outlets (or escapes). The inlet and outlet structures must also be provided with energy dissipators wherever necessary. Fig Level crossing

4 AQUEDUCTS AND CANAL INLETS AND OUTLETS 421 The following worked example highlights the various aspects of the hydraulic design of a cross-drainage structure. Worked Example 10.1 Design a siphon aqueduct for the following data: Canal Stream Discharge (m 3 s 1 ) Bed level (m AOD) Canal FSL (m AOD) Bed width (m) Canal side slopes 001.5:1V Stream HFL (m AOD) The general terrain level is m AOD. Solution DRAINAGE WATERWAY Perimeter P 4.75Q 1/2 (régime width, equation (9.9)) 106 m. Providing 12 piers of 1.25m thickness, we have 13 spans of 7m each. Therefore waterway provided m (satisfactory). Assuming a maximum velocity through the siphon barrels of 2ms 1, height of barrel 500/(13 7 2) 2.747m. Provide rectangular barrels, 7 m wide and 2.75m high (shown in Fig.10.5). CANAL WATERWAY Since the drainage width is large (106m at the crossing) it is economical to flume (concrete, n 0.014) the canal. Adopt a maximum flume ratio of 0.5. Therefore the flumed width of the canal (trough) m. Providing a splay of 2:1 in contraction and a splay of 3:1 in expansion (Hinds, 1928), length of transitions in contraction 12.5 m, length of transitions in expansion m. The length of the trough from abutment to abutment 106m. DESIGN OF FLUMED SECTION WITH TRANSITIONS Referring to Fig. 10.3, the following results can be obtained to maintain a constant depth of flow of 2.0m (given). The calculations are achieved from section 44 and proceed towards section 11 as tabulated below:

5 422 CROSS-DRAINAGE AND DROP STRUCTURES Fig.10.3 Transition with cylindrical inlet and linear outlet. L c and L e are contraction and expansion lengths Section Width (m) Area of flow (m 2 ) Velocity (m s 1 ) Losses (m) (expansion) (friction) (contraction) Water surface level (m AOD) Velocity head (m) TEL (m AOD) Flow depth (m) Bed level (m AOD) Note that the contraction loss 0.2(V 2 2 V 2 1)/2g; the expansion loss 0.3 (V 2 3 V 2 4)/2g; the flume friction loss V 2 f n 2 L f /R 4/3 f (the suffix f denotes the flume, and o the original canal V f V 3 V 2 ; V o V 4 V 1 ). DESIGN OF TRANSITIONS For a constant depth of flow the transition may be designed such that the rate of change of velocity per metre length of transition is constant. This approach yields the bed width of the transition at a distance x from the flume section as B x B o B f L/[LB o (B o B f )x]

6 AQUEDUCTS AND CANAL INLETS AND OUTLETS 423 which, modified after experimental studies (UPIRI, 1940), gives x LB o 3/2 [1 (B f /B x ) 3/2 ]/(B o 3/2 B f 3/2 ) where L is length of the transition. The following table shows the calculated geometries of the transition provided: B x (m) x (m) (contraction) x (m) (expansion) The transitions are streamlined and warped to avoid any abrupt changes in the width. Transitions with a cylindrical inlet with an average splay of 2:1 and a linear outlet with a splay of 3:1 provided with flow deflectors (Fig. 10.3; Ranga Raju, 1993) have been found to perform better than lengthy curved expansions. As the flow is accelerating in a contracting transition and the energy loss is minimal any gradual contraction with a smooth and continuous boundary should be satisfactory, e.g. an elliptical quadrant is an alternative to a cylindrical quadrant for inlet transitions. The bedline profile for an elliptical quadrant transition has the equation x 2 y 2 1 2(Bo B f ) and the length of transition given by L c 2(B o B f ). At any location (x) from flume end of the transition y is computed and the bed width B x calculated by B x B o 2y. 0.5(Bo B f ) The side slope (m) of the transition (m 0 for flume section and m 2 for canal side slope) and bed elevation may be varied linearly along the transition length. The expansion experiences considerable energy loss and care must be exercised in designing a hydraulically satisfactory transition. On the basis of theoretical and experimental investigations Vittal and Chiranjeevi (1983) proposed the following design equations for bed width and the side slopes of an expanding transition. The bed widths B x are fixed by

7 424 CROSS-DRAINAGE AND DROP STRUCTURES where B x B f B0 B f x 1 x 1 n n m o 1/2 and the transition length, L 2.35(B 0 B f ) 1.65m o y o, y o being the flow depth in the canal, and m o its side slope. The side slopes (m) along the transition are given by m m 1 1 L x 1/2. o L L Using the constant specific energy condition in the transition between canal and flume the depth in the flume, y f, and depths (y x ) along the transition length can be obtained. The energy balance between adjacent sections within the transition with expansion loss as 0.3(V 2 i V 2 i 1)/2g gives the bed elevations to be provided at successive sections so that the specific energy remains constant throughout the transition. Worked example 10.2 provides detailed design calculations for an expanding transition based on the Vittal and Chiranjeevi method. WATER SURFACE PROFILE IN TRANSITION The water surface in the transition may be assumed as two smooth parabolic curves (convex and concave) meeting tangentially. Referring to Fig.10.4, the following equations give such profiles in transitions: inlet transition, y x 2 ; outlet transition, y x 2. Fig Water surface profile in transition (inlet)

8 AQUEDUCTS AND CANAL INLETS AND OUTLETS 425 A highway 6m wide is provided alongside the canal by dividing the flume into two compartments by a 0.3m thick partition. The entire trough (flume section) can be designed as a monolithic concrete structure. Provide side walls and a bottom slab of about 0.4m (to be fixed by the usual structural design methods). SIPHON BARRELS Thirteen barrels, each 7m wide and 2.75m high, are provided; assume that the effective roughness, k 0.6mm (concrete). The length of the barrel, L m. The head loss through the barrel, h f (1.5 L/4R)V 2 /2g. The velocity through the barrel, V 500/( ) 1.998ms 1. The hydraulic radius, R /{2(7 2.75)} 0.987m. Therefore the Reynolds number 4VR/v and k/4r Hence, from Moody s chart, the friction factor 0.015, giving h f 0.316m. Therefore, the upstream HFL m AOD. The uplift pressures on the roof of the barrel are as follows. The RL of the bottom of the trough m AOD. The entry loss at the barrel 0.5V 2 /2g 0.102m. Therefore the pressure head inside the barrel just downstream of its entry m 11kNm 2. The most critical situation arises when the canal is empty and the siphon barrels are full. The weight of the roof slab kNm 2 (assuming the relative density of concrete to be 2.4). Hence the roof slab needs additional reinforcement at its top to resist the unbalanced pressure forces (uplift pressures). The total weight of the trough (when empty) needs to be checked against the total upward force and suitable anchorages to piers provided, if necessary. Equally, the trough floor slab has to be checked when it is carrying water at FSL and the level in the drainage is low, i.e. barrels running part full. The uplift on the floor of the barrel (assuming the barrel floor thickness to be 1m initially) is as follows: RL of the bottom of the barrel m AOD; RL of the drainage bed m AOD. Therefore the static uplift on the floor m (the worst condition with the water table as the drain bed level). The seepage head (a maximum when the canal is at FSL and the drainage is empty) m. In spite of the three-dimensional seepage flow pattern, Bligh s creep

9 426 CROSS-DRAINAGE AND DROP STRUCTURES length may be approximated as follows. Creep flow commences from the beginning of the upstream transition (downstream of this the floor is impervious) and enters the first barrel floor; from its centre the flow follows downstream of the drain and emerges at the end of the impervious concrete floor of the barrel. Therefore the total creep length can be approximated as inlet transition length barrel span length of barrel impervious floor. Let us assume that the total length of the impervious floor of the barrel is 25m, consisting of the following: length of barrel m pier projections, m downstream ramp (1:5), m upstream and downstream cut-offs, m total floor length m Therefore provide the upstream floor (1:3) length m. The total creep length /2 25/ m. The creep length up to the centre of the barrel /2 16.0m. Therefore the seepage head at the centre of the barrel 4(1 16.0/28.5) 1.75 m. The total uplift is then m 38kNm 2, and the weight of the floor kNm 2. Hence additional reinforcement has to be designed to resist the unbalanced uplift forces. UPSTREAM AND DOWNSTREAM PROTECTION WORKS The scour depth, R s (regime scour depth, equation (9.10)) 0.47(500/1) 1/3 3.73m. The upstream cut-off below HFL 1.5R 5.6m. Therefore RL of upstream cut-off wall (say) m AOD. The downstream cut-off below HFL 1.75R s 6.53 m. Therefore RL of downstream cut-off wall (say) m AOD, downstream apron length 2.5( ) 10 m, upstream apron length 2.0( ) 6m. The detailed layout (longitudinal section) of the design is shown in Fig

10 AQUEDUCTS AND CANAL INLETS AND OUTLETS 427 Fig metres Longitudinal section of the siphon aqueduct; all dimensions in Worked Example 10.2 Design an expanding transition for the flume canal layout of worked example 10.1 using the Vittal and Chiranjeevi (1983) method. Solution Design discharge 30m 3 s 1 ; bed width of canal, B o 25m; bed width of flume, B f 12.5m; side slope of canal, m o 1.50; bed level of canal m AOD; depth of flow in canal, y o 2m (Worked example 10.1). Length of transition, L 2.35( ) m. Bed width in transition, B x, with n (1.5) 1/ , B x 12.5 (12.5x/36)[1 (1 x/36) ]. Side slope in transition, m 1.5[1 (1 x/36) 1/2 ]. The complete set of calculations is presented in the table below: Number Distance from upstream y x (m) m B x (m) z Bed elevation end of transition, x (m) (m) (m AOD)

11 428 CROSS-DRAINAGE AND DROP STRUCTURES 10.2 Culverts, bridges and dips Introduction Highways cross natural drainage channels or canals, and provision must be made for appropriate cross-drainage works. The alignment of a highway along ridge lines (though it may be a circuitous route with less satisfactory gradients) may eliminate the cross-drainage work, thus achieving considerable savings. Highway cross-drainage is provided by culverts, bridges and dips. Culverts are usually of shorter span ( 6m), with the top not normally forming part of the road surface like in a bridge structure. They are submerged structures buried under a high-level embankment. On the other hand, if the embankment is a low-level one, appropriate armouring protection works against overtopping during high floods have to be provided. Such a low-level structure (sometimes called a dip ) in the absence of the culvert is often economical if the possible traffic delays do not warrant a costly high-level structure such as a bridge, keeping the road surface above all flood levels. A culvert combined with a dip (lowered road surface) is an attractive solution for small perennial streams with occasional flash floods; however, appropriate traffic warning systems/signs have to be incorporated. Bridges are high-level crossing structures which can be expensive for large rivers. It is therefore essential to protect them even from rare floods. It is often advantageous to allow overtopping of part of the approach embankment, which may act as a fuse plug, to be replaced if necessary, after the flood event. Such an alternative route for the water avoids the overtopping of the bridge deck and, in addition, reduces the scouring velocities which may otherwise undermine the foundations of the structure Culverts The culvert consists essentially of a pipe barrel (conveyance part) under the embankment fill, with protection works at its entrance and exit. At the entrance a head wall, with or without wing walls, and a debris barrier are normally provided. If necessary, an end wall with energy-dissipating devices is provided at the exit. The culvert acts as a constriction and creates a backwater effect to the approach flow, causing a pondage of water above the culvert entrance. The flow within the barrel itself may have a free surface with subcritical or supercritical conditions depending on the length, roughness, gradient, and upstream and downstream water levels of the culvert. If the upstream head is sufficiently large the flow within the culvert may or may not fill the barrel, and its hydraulic performance depends upon the combination of entrance and friction losses, length of barrel, and the downstream backwater effects (Fig.10.6).

12 CULVERTS, BRIDGES AND DIPS 429 Fig Flow through a culvert The various flow types that can exist in the pipe barrel of a culvert are shown in Table The hydraulic design of the culvert is based on the characteristics of the barrel flow, and Worked examples 10.3 and 10.4 highlight calculations involving all the six types of flow listed in Table Table 10.1 Types of flow in the barrel of a culvert (Chow, 1983) Type H/D Exit depth Flow type Length Slope Control Remarks y 2 L S 0 Submerged entrance conditions D Full Any Any Outlet Pipe flow D Full Long Any Outlet Pipe flow D Part full Short Any Outlet Orifice Free entrance conditions D Part full Any Mild Outlet Subcritical critical D Part full Any Mlld Outlet Subcritical critical D Part full Any Steep Inlet Supercritical critical critical Formation of hydraulic jump in barrel The reader is referred to Ramsbottom et al. (1997), Chanson (1999) and Mays (1999) for additional information on culvert flows, establishment of stage discharge relationships and culvert design in general. Charbeneau et al. (2006) use a two parameter model describing the hydraulic performance of highway culverts operating under inlet control for both unsubmerged and submerged conditions. The hydraulic performance of a culvert can be improved by the adoption of the following guidelines.

13 430 CROSS-DRAINAGE AND DROP STRUCTURES (a) Culvert alignment As a general rule, the barrel should follow the natural drainage alignment and its gradient, in order to minimize head losses and erosion. This may lead to a long skew culvert which will require more complex head and end walls. However, it is sometimes more economical to place the culvert perpendicular to the highway with certain acceptable changes in the channel alignment (see Linsley and Franzini, 1979). (b) Culvert entrance structures Properly designed entrance structures prevent bank erosion and improve the hydraulic characteristics of the culvert. The various types of entrance structures (end walls and wing walls) recommended are shown in Fig Fig Culvert entrance structures; plan views

14 CULVERTS, BRIDGES AND DIPS 431 A debris barrier (trash rack) must also be provided upstream of the culvert entrance to prevent the blockage of the barrel entrance. In the case of a culvert with a submerged entrance, flaring the entrance will increase its capacity under a lower head for a given discharge. Such an arrangement for a box culvert (square or rectangular concrete barrel), the entrance area being double the barrel area over a length of 1.2D, where D is the height of the barrel, is shown in Fig A drop inlet structure with a necessary debris barrier (timber or concrete cribs) has to be provided whenever the culvert entrance is at the bed level (highway drainage facilities) of the drainage, requiring an abrupt break in the channel slope. Various arrangements of drop inlet culverts are shown in Fig The culvert sill length must be sufficient to discharge the design flow with a reasonably low-head water level. For high discharges, the entrance may be flared so as to increase the crest length. A flared entrance with a back wall (to prevent vortex action) considerably increases the inlet capacity. De-aeration chambers may have to be provided if a jump forms in the barrel of the culvert. Fig Box culvert with flared entrance

15 432 CROSS-DRAINAGE AND DROP STRUCTURES Fig Drop inlet culvert (c) Culvert outlet structures A proper device has to be provided at the outlet of a culvert to prevent the downstream erosion of the bed and the slopes of the embankment. For small discharges a straight or U-shaped end wall is sufficient. For moderate flows a flaring wing-walled outlet connecting the much wider downstream channel will reduce the scouring of the embankment and channel banks. The suggested flare angle for supercritical flows should be under 1 in 2, decreasing linearly with the flow Froude number. For subcritical flows it may be larger than 1 in 2. (d) Scour below culvert outlets The flow through a culvert may cause undesirable erosion (scour) at its unprotected outlet which can lead to undermining of the culvert structure.

16 CULVERTS, BRIDGES AND DIPS 433 Several researchers performed model tests on scour downstream of culvert structures and the combined results suggest the following design guidelines (see Breusers and Raudkivi, 1991): scour depth below bed level, y s 0.65D(U o /U *c ) 1/3 (10.1) where U o flow velocity at exit and U *c Shields critical shear velocity ( ( c / ) 1/2 ); scour width, B s 7.5DF r 2/3, (10.2) scour length, L s 15DF r 2/3 (10.3) where D culvert height, F r U 0 /(gd) 1/2, 0.27 F r 2.7 and 0.22 d (mm) 7.3. Equation (10.1) may be modified in the case of graded material as y s 3.18DF 0.57 d r D 0.4 g (10.4) where g (d 84 /d 16 ) 1/2. In order to protect the channel bed against scouring, a minimum stone size is recommended as d s 0.25DF r (10.5) for low tail water levels. For high tail water levels ( D/2) the recommended stone size is reduced by 0.15D. Fletcher and Grace (1974) recommended a lining of trapezoidal cross-section downstream of the culvert exit extending to a length 5D with a bed slope of 1 in 10 followed by a curtain wall to a length D at a slope of 1 in 2; the side slopes of the trapezoidal lining are recommended to be 1 in 2. Alternatively, the design curves of Simons and Stevens (1972) may be used for non-scouring and scouring bed protection in rock basins (see Breusers and Raudkivi, 1991). Blaisdell and Anderson (1988a, b) made a comprehensive study of scour at cantilevered pipe outlets and suggested the ultimate maximum scour hole depth, Z max, below tailwater level (zero elevation) as Z max 7.5[1 e 0.6(F rd 2) ] (10.6) D for Z p /D 1 and Z max 10.5[1 e 0.35(F rd 2) ] (10.7) D

17 434 CROSS-DRAINAGE AND DROP STRUCTURES for Z p /D 1 where D pipe diameter, Z p height of pipe outlet above tailwater level and F rd V/(g d 50 ) 1/2, V being the jet plunge velocity at the tailwater (F rd 2; 2 Z p (m) 8; outlet slope, ). The usual energy-dissipating devices (sloping apron, cistern, stilling basin, plunge pool, etc.) may have to be provided if the culvert discharge velocities are very high (Chapter 5) Bridges The presence of a bridge across a stream creates constricted flow through its openings because of (a) the reduction in the width of the stream due to piers and their associated end contractions and (b) the fluming of the stream itself (in the case of wide streams with flood plains) to reduce the costs of the structure. Apart from (local) scour around the piers and bridge abutments and possible bed erosion, there is a considerable backwater effect of the bridge. The corresponding afflux (rise in upstream water level) depends on the type of flow (subcritical or supercritical). As most bridges are designed for subcritical flow conditions in order to minimize scour and choking problems, further discussions here are mainly confined to subcritical flow. The establishment of afflux levels is extremely important for the design of upstream dykes and other protective works and also for the location of safe bridge deck levels (to avoid the flooding of the deck and any consequent structural damage). It is equally important to determine the minimum clear length of span (economic considerations) which will not cause undesirable afflux levels. In order to establish permissible upstream stage levels, detailed investigations of the properties along the stream have to be investigated. Downstream of the bridge the water levels are only influenced by the nearest control section below the bridge. These levels can therefore be established by backwater computation (for further information see Hamill, 1999). (a) Backwater levels SHORT CONTRACTIONS In flow through a relatively short contracted section (narrow bridge without approach fluming) with only a few piers, the backwater problem may be relatively less important. Referring to Fig , the change in

18 CULVERTS, BRIDGES AND DIPS 435 Fig Flow profile through bridge with contracted channel of relatively short length (subcritical flow) water level, h, can be obtained by the energy equation between sections 1 and 2 (Kindsvater, Carter and Tracy, 1953) as h K B V 2 2/2g S 0 L/ 1 V 2 1/2g (10.8) where K B is the bridge loss coefficient (Table 10.2), expressed as a function of the conveyance ratio, k b /k B, (10.9) Table 10.2 Bridge loss coefficient, K B K B

19 436 CROSS-DRAINAGE AND DROP STRUCTURES k b being the conveyance of the gross contracted section with the same normal depth and roughness characteristics as the upstream approach section whose conveyance is k B. For rectangular unflumed sections the conveyance ratio (contraction ratio, 1 ) becomes b/b, b being the clear width of the stream (of normal width, B) under the bridge (Fig.10.10). The bridge loss coefficient is also a function of the geometry of the bridge, its skew and eccentricity, and the submergence of the superstructure (i.e. the deck). V 2 is the velocity just downstream of the piers, using the gross area under the bridge with the same upstream normal depth, and 1 is the energy correction coefficient of the approach section. L is assumed to be equal to the bridge length (abutment to abutment), and S 0 is the normal bedslope of the unobstructed steam. LONG CONTRACTIONS In the case where the bridge has a number of large piers and/or long approach embankments contracting the water width, the backwater effect is considerable. Referring to the flow profile shown in Fig , through such a long contracting section, y is the afflux entirely created by the presence of piers and channel contraction. Momentum and continuity equations between sections 1 and 3 (assuming hydrostatic pressure distribution with a negligible bed slope and frictional resistance) result in where y/y 3 {A [A 2 12C D (b/b)fr 2 3] 1/2 }/6 (10.10) A {C D (b/b) 2}Fr (10.11) Fr 3 being the Froude number ( V 3 /(gy 3 ) 1/2 ) at section 3. Equation (10.10) should give good results if the drag coefficient C D can be accurately estimated. The pier drag coefficient has been found to be a function of the velocity gradient of the approach flow, b/b, and the pier shape; however, owing to the non-availability of reliable drag coefficient values, the use of equation (10.10) is limited. Yarnell s (1934) experimental data on the flow through bridge piers resulted in the following empirical equation: where y/y 3 KFr 2 3(K 5Fr )( 15 4 ) (10.12) 1 1 b/b (10.13) and K is a function of the pier shape according to Table 10.3.

20 CULVERTS, BRIDGES AND DIPS 437 Table 10.3 Values of K as a function of pier shape Pier shape K Remarks Semicircular nose and tail 0.9 } All values applicable for piers Lens-shaped nose and tail 0.9 with length to breadth ratio Twin-cylinder piers with connecting equal to 4; conservative diaphragm 0.95 estimates of y have been found for larger ratios; Twin-cylinder piers without diaphragm 1.05 } Lens-shaped nose is formed 90 triangular nose and tail 1.05 from two circular curves, each of radius to twice the Square nose and tail 1.25 pier width and each tangential to a pier face Equation (10.12) is valid only if is large, i.e. the contraction cannot set up critical flow conditions between piers and choke the flow. If the flow becomes choked by excessive contraction the afflux increases substantially (Fig.10.11). Referring to Fig.10.11, the limiting values of (assuming uniform velocity at section 2) for critical flow at section 2 can be written as (2 1/ ) 3 Fr 4 3/(1 2Fr 2 3) 3. (10.14) In the case of choked flow the energy loss between sections 1 and 2 was given by Yarnell as E 1 E 2 C L V 2 1/2g (10.15) where C L is a function of the pier shape (equal to 0.35 for square-edged piers and 0.18 for rounded ends, for a pier length:width ratio of 4). From equation (10.15) the upstream depth, y 1, can be calculated, from which the afflux y is obtained as y 1 y 3. Skewed bridges produce greater affluxes, and Yarnell found that a 10 skew bridge gave no appreciable changes, whereas a 20 skew produced about 250% more afflux values. For backwater computations of arch bridges Martín-Vide and Prió (2005) recommend a head loss coefficient K for the sum of contraction and Fig Flow profile with choked flow conditions

21 438 CROSS-DRAINAGE AND DROP STRUCTURES expansion losses as K 2.3m 0.345, where m is the ratio of the obstructed and channel areas for m (b) Discharge computations at bridge piers 1. Nagler (1918) proposed a discharge formula for subcritical and nearcritical flows as follows: Q K N b(2g) 1/2 (y 3 V 2 3/2g)(h 3 V 2 1/2g) 1/2 (10.16) the notation used in equation (10.16) being shown in Fig.10.12(a). K N is a coefficient depending on the degree of channel contraction and on the characteristics of the obstruction (Table 10.4); is a correction factor intended to reduce the depth y 3 to y 2 and is the correction for the velocity of approach, depending on the conveyance ratio (Fig.10.12(b)). 2. d Aubuisson (1940) suggested the formula Q K A b 2 y 3 (2gh 3 V 2 1) 1/2 (10.17) where K A is a function of the degree of channel contraction and of the shape and orientation of the obstruction (Table 10.4). d Aubuisson made no distinction between y 3 and y 2, and, although in many cases there is a small difference between them, equation (10.17) is recognized as an approximate formula. 3. Chow (1983) presents a comprehensive discussion of the discharge relationship between the flow through contracted openings and their shape, and other characteristics, together with a series of design charts produced by Kindsvater, Carter and Tracy (1953). Fig Discharge computations through obstructions (definition sketch)

22 CULVERTS, BRIDGES AND DIPS 439 Table 10.4 Values of K N and K A Type of pier Conveyance ratio, K N K A K N K A K N K A K N K A K N K A Square nose and tails Semicircular nose and tails triangular nose and tails Twin-cylinder piers with or without diaphragms Lens-shaped nose and tails (c) Scour depth under the bridge If the contracted width (i.e. the bridge length, L) is less than the régime width, W (equation (9.9)), the normal scour depth, D N, under the bridge is given by D N R s (W/L) 0.61 (10.18) where R s is the régime scour depth (equation (9.10)). The maximum scour depth in a single-span bridge (no piers) with a straight approach (case 1) is about 25% more than the normal scour given by equation (10.18), whereas in the case of a multispan structure with a curved approach reach (case 2) it is 100% more than the normal scour. If the constriction is predominant, the maximum scour depth is the maximum of case 1 or case 2, or the value given by D max R s (W/L) (10.19) (d) Scour around bridge piers Several formulae based on experimental results have been proposed to predict the maximum or equilibrium scour depth (y s, below general bed level) around bridge piers. In general, these assume the relationship y s /b (y 0 /b, Fr, d/b ) (10.20) where b is the pier width, y 0 is the upstream flow depth, d is the sediment size, and Fr is the flow Froude number.

23 440 CROSS-DRAINAGE AND DROP STRUCTURES Laursen s (1962) experimental results underestimate the scour depths, compared to many Indian experiments (Inglis, 1949) which suggest the formula (approach flow is normal to the bridge piers) y s /b 4.2(y 0 /b ) 0.78 Fr (10.21) The Indian field data also suggest that the scour depth should be taken as twice the régime scour depth. In the case of live beds (a stream with bedload transport) the formula y s /y 0 (B/b ) 5/7 1 (10.22) predicts the maximum equilibrium scour depth. In a relatively deep flow a first-order estimate of (clear) local scour (around pier) may be obtained by y s 2.3K b (10.23) where K angularity coefficient which is a function of the pier alignment, i.e. angle of attack of approach flow. Once again the best estimate will be achieved with the appropriate coefficients for flow depth, alignment, etc. (see Breusers and Raudkivi (1991) for further information). The live bed, however, contributes to an appreciably reduced local scour depth. If the sediment bed is distinctly layered and the covering layer (normally coarse material) is of a thickness less than the local scour depth the overall scouring phenomenon is quite different (see Ettema, 1980). The flow penetrates the covering layer, triggering its disintegration. The disintegration of the covering layer may at times take place only in the downstream direction, leaving a stepped scour just upstream of the pier followed by a further local pier scour at its bottom. The stepped scour depth in the covering layer, H, is given by H (y 2 y 1 ) (10.24) where y 1 and y 2 are the uniform flow depths over a flat bed of grain roughness corresponding to the upstream surface particles (d 1 ) and the underlying surface fine particles (d 2 ) respectively; the coefficient for non-ripple-forming sediments 2.6 for design purposes. The total scour depth may lead to a gross underestimate if the lower layer is of very fine material (which may go into suspension). The whole field of scour at bridge piers, piles and abutments is the subject of ongoing research focussing particularly on large scale experiments and development of scour with time. To proceed further with this topic is beyond the scope of this book and the reader is referred to e.g.

24 CULVERTS, BRIDGES AND DIPS 441 Breusers, Nicollet and Shen (1977), Clark and Novak (1983), Richardson and Richardson (1994), Melville and Chiu (1999), Melville and Coleman (2000), Oliveto and Hager (2002), Coleman, Lauchlan and Melville (2003), Sheppard, Odeh and Glasser (2004) and Dey and Barbhuiya (2005). (e) Scour protection works around bridge piers Although the presence of scour tends to reduce the backwater levels upstream of the bridge, the damage to the foundations of the structure may far outweigh the possible benefit. Hence protective measures, both to minimize the scour and to prevent undermining of the foundations, have to be taken. Piers with base diaphragms (horizontal rings) and multiple cylinder type piers have been found to minimize the scour considerably. The normal practice for protection of the foundation is to provide thick protective layers of stone or concrete aprons around the piers. A riprap protection (Bonasoundas, 1973) in the shape of a longitudinal section of an egg with its broader end facing the flow is recommended for a cylindrical pier. The recommended overall width is 6b and length 7b of which 2.5b is upstream of the pier. The thickness of riprap is 1/3b with a maximum stone size, d, given by d U 0.04U 2 (10.25) with U in metres per second and d in metres. The mean critical flow velocity U c (m s 1 ) with a flow depth y 0 (m) is given by U c 6d 1/3 y 0 1/6 (10.26) d being the armour stone size in metres (with s 2600kgm 3 ). For horizontal beds (US Army Coastal Engineering Research Center (1984); Chapter 14) the simplified empirical relationship is U c 4.92d 1/2. (10.27) The riprap should be placed on a suitable inverted filter or a geotextile fabric (Fig.9.11). For further discussion of scour protection works refer to Zarrati et al. (2006) and Unger and Hager (2006). For a comprehensive treatment of bridge hydraulics (including hydraulic aspects of bridge construction and maintenance) refer to Neill (2004).

25 442 CROSS-DRAINAGE AND DROP STRUCTURES Dips The dip is a shallow structure without excessive approach gradients. In arid regions, streams with infrequent flash floods and shallow depths ( 0.3m) may be allowed to flow through the dipped area. The upstream road edge should not be discontinuous with the stream bed in order to avoid scour, and at the downstream edge protection works such as a cutoff wall, concrete, or riprap paving must be provided. Also, the profile of the dip should, as far as possible, conform to the profile of the stream to minimize local disturbances to the flow. The road surface has to withstand the expected flow velocities and debris. Bitumen-bound macadam may withstand velocities of up to 6 ms 1, whereas up to 7ms 1 may be permitted on asphalted road surfaces. Lowlevel embankments, where occasional overtopping is permitted, must be protected against scour and bank-slope stability. The permissible mean velocities for a range of protective materials are suggested in Table 10.5 (Watkins and Fiddes, 1984). The overflow discharge over an embankment may be predicted by using the weir formula of the type Q CbH 3/2 (9.29) where C is the sill coefficient (m 1/2 s 1 ), b is the length of the flow section and H is the total head upstream of the sill. The coefficient C is a function of h/l (h is the head over a sill of width L) for free flow conditions. For non-modular flow conditions a correction factor, f, as a function of h d/s /H, may be incorporated in equation (9.29) (Tables 10.6 and 10.7). Table 10.5 Permissible velocities to withstand erosion Type of protection Velocity (ms 1 ) Grass turfing: Bermuda grass 2.0 buffalo grass 1.5 Cobbles: 100 mm mm 2.5 Coarse gravel and cobbles ( 25mm) 2.0 Gravel ( 10 mm) 1.5

26 CULVERTS, BRIDGES AND DIPS 443 Table 10.6 Range of values of C for free flow over the embankment Type of surface Range of h/l Range of C Paved surface Gravel surface Table 10.7 Correction factor, f (non-modular flows) Type of surface Range of h d/s /H f Paved surface Gravel surface Worked Example 10.3 Establish the stage (headwater level) discharge relationship for a concrete rectangular box culvert, using the following data: width 1.2m; height 0.6m; length 30m; slope 1 in 1000; Manning s n 0.013; square-edged entrance conditions; free jet outlet flow; range of head water level for investigation 0 3m; neglect the velocity of approach. Solution 1. H/D 1.2. For H 0.6m, free flow open-channel conditions prevail. Referring to Fig.10.6 and assuming that a steep slope entry gives entrance control, i.e. the depth at the inlet is critical, for H 0.2 m, ignoring entry loss y c (2/3) m and V c 1.142ms 1. This gives the critical slope (Vn) 2 /R 4/ Therefore the slope of the culvert is mild and hence subcritical flow analysis gives the following results: Q 1.2y 0 [1.2y 0 /(1.2 2y 0 )] 2/3 (0.001) 1/2 / y 0 [1.2y 0 /(1.2 2y 0 )] 2/3 ; (i)

27 444 CROSS-DRAINAGE AND DROP STRUCTURES y 0 (m) Q (m 3 s 1 )(equation (i)) y c (m) ( D) At the inlet over a short reach, H y 0 V 2 /2g K e V 2 /2g. (ii) The entrance loss coefficient, K e, is as follows: for a square-edged entry, 0.5; for a flared entry, 0.25; for a rounded entry, 0.05; y 0 (m) H (m) (equation (ii)) Q (m 3 s 1 ) orifice 0.6 (1.2D ) (by interpolation) 2. H/D 1.2. (a) For orifice flow Q C d ( )[2g(H D/2)] 1/2. (iii) With C d 0.62 the following results are obtained: H(m) Q (m 3 s 1 ) y 0 (m) (equation (i)) no orifice flow exists (b) For pipe flow the energy equation gives H S 0 L D h L where h L K e V 2 /2g (Vn) 2 L/R 4/3 V 2 /2g. Thus Q 2.08(H 0.57) 1/2. (iv)

28 CULVERTS, BRIDGES AND DIPS 445 H (m) Q (m 3 s 1 ) (equation (iv)) y (equation (i) During rising stages the barrel flows full from H 0.72 m and during falling stages the flow becomes free-surface flow when H m. The following table summarizes the results: H (m) Q (m 3 s 1 ) Type of flow Rising stages Open channel Open channel Open channel Pipe flow Pipe flow Pipe flow Pipe flow Falling stages Pipe flow Pipe flow Pipe flow Pipe flow Open channel Open channel Open channel Worked Example 10.4 Examine the stage discharge relationship for the culvert in Worked example 10.3 if the bedslope is 1 in 100. Solution Rising stages are as follows. 1. For the open channel, preliminary calculations now indicate that the slope is steep and hence the entrance is the control, with the critical depth at the entry. The energy equation at the inlet gives H 1.5V 2 /2g y 1.75y c. (v)

29 446 CROSS-DRAINAGE AND DROP STRUCTURES y c (m) H (m) Type Q (m 3 s 1 ) Free Free ( 1.2D) Submerged ( 1.2D) Just free For the orifice (equation (iii)), H (m) Type Q (m 3 s 1 ) y 0 (m) (equation (i) with S 0 1/100)* 0.72 Orifice Orifice Orifice? ( D) 1.95 Orifice *Q 9.23y 0 [1.2y 0 /(1.2 2y 0 )] 2/3 3. For pipe flow (equation (iv) changes): Q 2.08(H 0.3) 1/2 for S 0 1/100. H (m) Type Q (m 3 s 1 ) y 0 (m) (equation (i)) 1.95 Pipe flow Pipe flow Pipe flow 3.42 Falling stages 3.00 Pipe flow Pipe flow Pipe flow Pipe flow Orifice Orifice Orifice Just free Free Free Worked Example 10.5 The design flood with a 20-year return period is 15m 3 s 1. Design the culvert-type cross-drainage structure with a high embankment with the following data: culvert length 30m; slope 1.5%; available pipe barrel, corrugated pipes in multiples of 250mm diameter; Manning s n The barrel protrudes from the embankment with no end walls, with an entry loss coefficient of 0.9. The maximum permissible head water level is 4m above the invert with the barrel flowing full.

30 CULVERTS, BRIDGES AND DIPS 447 Solution For full pipe flow the energy equation gives H D 0.9V 2 /2g (Vn) 2 L/R 4/3 V 2 /2g. (vi) Equation (vi) gives the following results: D (m) H (m) Therefore provide a 2.25m diameter barrel for H 4.0m. Check for the flow conditions: H/D 3.70/ Hence the inlet is submerged. Using Manning s equation with the maximum discharge, the required diameter for the flow to be just free is 2.32 m, which is greater than the diameter provided. Hence the barrel flows full (under pressure). Note that an improved entrance would considerably reduce the head loss and allow a smaller-diameter barrel to discharge the flood flow. For example a flare-edged entry (loss coefficient 0.25) would produce a head of 3.93m ( 4.0m) with a barrel of 2.00m diameter. Worked Example 10.6 A road bridge of seven equal span lengths crosses a 106m wide river. The piers are 2.5m thick, each with semicircular noses and tails, and their length:breadth ratio is 4. The streamflow data are given as follows: discharge 500m 3 s 1 ; depth of flow downstream of the bridge 2.50 m. Determine the afflux upstream of the bridge. Solution The velocity at the downstream section, V 3 500/ ms 1. Therefore the Froude number, Fr Flow conditions within the piers are as follows: the limiting value of 0.55 (equation (10.14)), while the value of provided b/b 13/ Since the value of provided is more than the limiting value, subcritical flow conditions exist between the piers. Using equation (10.12) with K 0.9 (Table 10.3) and , the afflux, y m.

31 448 CROSS-DRAINAGE AND DROP STRUCTURES 10.3 Drop structures Introduction A drop (or fall) structure is a regulating structure which lowers the water level along its course. The slope of a canal is usually milder than the terrain slope as a result of which the canal in a cutting at its headworks will soon outstrip the ground surface. In order to avoid excessive infilling the bed level of the downstream canal is lowered, the two reaches being connected by a suitable drop structure (Fig.10.13). The drop is located so that the fillings and cuttings of the canal are equalized as much as possible. Wherever possible, the drop structure may also be combined with a regulator or a bridge. The location of an offtake from the canal also influences the fall site, with offtakes located upstream of the fall structure. Canal drops may also be utilized for hydropower development, using bulb- or propeller-type turbines. Large numbers of small and mediumsized drops are desirable, especially where the existing power grids are far removed from the farms. Such a network of micro-installations is extremely helpful in pumping ground water, the operation of agricultural equipment, village industries, etc. However, the relative economy of providing a large number of small falls versus a small number of large falls must be considered. A small number of large falls may result in unbalanced earthwork but, on the other hand, some savings in the overall cost of the drop structures can be achieved. Drops are usually provided with a low crest wall and are subdivided into the following types: (i) the vertical drop, (ii) the inclined drop and (iii) the piped drop. The above classification covers only a part of the broad spectrum of drops, particularly if structures used in sewer design are included; a comprehensive survey of various types of drops has been provided, e.g. by Merlein, Kleinschroth and Valentin (2002); Hager (1999) includes the treatment of drop structures in his comprehensive coverage of wastewater structures and hydraulics. Fig Location of canal drops

32 DROP STRUCTURES Vertical drop structures (a) Common (straight) drop The common drop structure, in which the aerated free-falling nappe (modular flow) hits the downstream basin floor, and with turbulent circulation in the pool beneath the nappe contributing to energy dissipation, is shown in Fig The following equations fix the geometry of the structure in a suitable form for steep slopes: drop number, D r q 2 /g d3 (10.28) where q is the discharge per metre width; basin length, L B /d 4.3D r 0.27 L j /d; (10.29) pool depth under nappe, Y P /d D r 0.22 ; (10.30) sequent depths, y 1 /d 0.54D r ; (10.31) y 2 /d 1.66D r 0.27 ; (10.32) here d is the height of the drop crest above the basin floor and L j the length of the jump. A small upward step, h (around 0.5 h/y 1 4), at the end of the basin floor is desirable in order to localize the hydraulic jump formation. Forster and Skrinde (1950) developed design charts for the provision of such an abrupt rise. The USBR (Kraatz and Mahajan, 1975) impact block type basin also provides good energy dissipation under low heads, and is suitable if the Fig Common drop structure (after Bos, 1976)

33 450 CROSS-DRAINAGE AND DROP STRUCTURES Fig Impact block type basin (after Bos, 1976) tailwater level (TWL) is greater than the sequent depth, y 2. The following are the suggested dimensions of such a structure (Fig ): basin length L B L d 2.55y c ; (10.33) location of impact block, L d 0.8y c ; (10.34) minimum TW depth, y y c ; (10.35) impact block height, 0.8y c ; (10.36) width and spacing of impact block, 0.4y c ; (10.37) end sill height, 0.4y c ; (10.38) minimum side wall height, y y c ; (10.39) here y c is the critical depth. The values of L d can be obtained from Fig Fig Values of L d /d (after Bos, 1976)

34 DROP STRUCTURES 451 (b) Sarda-type fall (India) This is a raised-crest fall with a vertical impact, consisting of a crest wall, upstream and downstream wing walls, an impervious floor and a cistern, and downstream bank and bed protection works (Fig.10.17). The crest design is carried out as follows. The crest length is normally kept equal to the bed width of the canal; however, an increase in length by an amount equal to the flow depth takes into account any future increase in discharge. Fluming may be provided to reduce the cost of construction of the fall. A flumed fall with a fluming ratio equal to 2F 1, where F 1 is the approach flow Froude number, creates no choking upstream of the fall. A canal is not usually flumed beyond 50%. Whenever the canal is flumed, both upstream (contracting) and downstream (expanding) transitions have to be provided (Fig.10.3). The crest level must be so fixed that it does not create changes in upstream water levels (backwater or drawdown effects). If the reduced level (RL) of the full supply level (FSL) is Y, the RL of the total energy line (TEL) is E Y V 2 a/2g (10.40) Fig Sarda fall layout (Worked example 10.7); dimensions in metres

35 452 CROSS-DRAINAGE AND DROP STRUCTURES where V a is the approach velocity. If L e is the effective length of the crest, the head causing flow is given by the weir formula: H (Q/C d L e ) 2/3 (10.41) where Q is the discharge and C d is the discharge coefficient of the crest. Therefore, the RL of the crest is E H. Two types of crest are used (Fig.10.18); the rectangular one for discharges up to 10m 3 s 1 and the trapezoidal one for larger discharges (see Punmia and Lal, 1977). The following are the design criteria established by extensive model studies at the Irrigation Research Institute in India. 1. For a rectangular crest, top width, B 0.55d 1/2 (m), (10.42) base width, B 1 (H d)/s s, (10.43) where S s is the relative density of the crest material (for masonry, S s 2). The discharge is given by the following formula: Q 1.835LH 3/2 (H/B) 1/6. (10.44) 2. For a trapezoidal crest, top width, B 0.55(H d) 1/2 (m). (10.45) For the base width, B 1, upstream and downstream slopes of around 1 Fig Sarda fall crests